Non Newtonian annular alloy solidification in mould

The annular solidification of an aluminium–silicon alloy in a graphite mould with a geometry consisting of horizontal concentric cylinders is studied numerically. The analysis incorporates the behavior of non-Newtonian, pseudoplastic (n?=?0.2), Newtonian (n?=?1), and dilatant (n?=?1.5) fluids. The fluid mechanics and heat transfer coupled with a transient model of convection diffusion are solved using the finite volume method and the SIMPLE algorithm. Solidification is described in terms of a liquid fraction of a phase change that varies linearly with temperature. The final results make it possible to infer that the fluid dynamics and heat transfer of solidification in an annular geometry are affected by the non-Newtonian nature of the fluid, speeding up the process when the fluid is pseudoplastic.     

A thermomechanical model for a 1-D shape memory alloy wire with propagating instabilities

A thermomechanical boundary value problem and constitutive model are presented for a shape memory alloy (SMA) wire under uniaxial loading. The intent is to develop a one-dimensional continuum model of an SMA element that includes all the relevant thermomechanical couplings and is suitable for inclusion in finite element analyses. Thermodynamic relations are derived from phenomenological considerations consistent with recent experimental observations and are calibrated to a typical commercially available NiTi wire material. The model includes both temperature-induced and stress-induced transformations that are necessary to exhibit the shape memory effect and pseudoelastic behaviors. The model accommodates possible unstable mechanical behavior during stress-induced transformations by allowing softening transformation paths and including strain gradient effects. This should provide a tool to study propagating transformation fronts and localized latent heat transfer with the surroundings and a variety of interesting future structural applications, such as composites with embedded SMA elements.     

A mathematical model for an alloy solidification problem in the presence of an electric field

A one-dimensional mathematical model for a process of solidification of a binary alloy in the presence of an electric field is studied. A situation in which the thermal properties of each phase are different and the latent heat is non-zero is considered. A quasi-static approximation for the thermal and electric fields is used. Local existence and uniqueness of a classical solution to the resulting free boundary problem are proved for two kinds of boundary conditions. Moreover, under particular hypotheses, the monotonicity of the free boundary and the global existence of the solution is proved.

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Sommario Si studia un modello matematico unidimensionale per un processo di solidificazione di una lega binaria in presenza di un campo elettrico. Si considera una situazione in cui le proprietà termiche di ogni fase sono differenti e il calore latente è non nullo. Si usa una approssimazione quasi-statica per i campi elettrico e termico. Si dimostra l'esistenza locale e l'unicità di una soluzione classica per il problema di frontiera libera risultante con due tipi di condizioni di bordo. Inoltre si dimostra, sotto particolari ipotesi, la monotonia della frontiera libera e l'esistenza di soluzione globale.

     

A theoretical model of matrix cracking in composite laminates under thermomechanical loading

A theoretical approach is presented for analyzing the ply cracking in general symmetric laminates subjected to any combination of in-plane mechanical loading and uniform temperature changes. The equivalent constraint model proposed by the authors in a previous work is used to account for the cracking interaction between laminae in the laminates. By using a superposition scheme and the stress field solutions the energy release rate for a ply cracking is explicitly expressed as a function of stiffness reduction parameters of the laminates. The ratio of mode I to mode II is introduced for construction of the fracture criterion. The effects of the laminate parameters and the crack spacing on the energy release rate and the mode mixity are illustrated. Finally, the model is used to predict the thermomechanical load for the first-ply-cracking. Project supported by the National Natural Science Foundation of China (No. 19972076) and the Germen Research Foundation (DFG).     

A dual-scale coupled micro/macro segregation model for dendritic alloy solidification

The present article reports on the formulation, numerical implementation, and application of a single-domain coupled micro/macroscopic model for simulation of dendritic alloy solidification. Microscopic solutal non-equilibrium effects have been included in the macroscopic modeling of solidification by using a fixed grid dual scale numerical approach. Salient features of the present approach include a continuum model for conservation of mass, momentum, energy and species on the macroscopic scale, a microscopic solute redistribution model, and the solution procedure and auxiliary equations necessary for coupling between the two models. The coupling between macro and micro scale models is practically made possible by introducing an iterative micro/macro time step scheme. The local solidification rate is calculated by implicit iterations of macroscopic conservation equations and the microscopic solute redistribution model. The present model is capable to simulate eutectic reaction, local re-melting, and account for the inter-linkage between micro and macroscopic solute redistribution (micro and macrosegregation).     

A length-dependent model for the thermomechanical response of ceramics

We present a length-dependent model for the thermomechanical response of ceramics through a concurrent multiscale scheme that accounts for: (i) the locally varying values of the sub-grain thermal conductivity tensor due to the interaction of phonons with microstructural features such as grain boundaries, and (ii) a continuum model of thermal stresses that explicitly resolves the polycrystalline structure of the material. At the sub-grain level, we compute the values of the thermal conductivity tensor using the Boltzmann transport equation under the relaxation time approximation. At the continuum level, the polycrystalline structure of the specimen is resolved explicitly by a finite element mesh and the texture of the polycrystal is assumed to be given. At this level, we adopt a Fourier model of heat conduction which utilizes values of thermal conductivity obtained at the lower scale. The mechanical response of the grains is modeled as elastic and anisotropic. The capabilities of the model are demonstrated through a series of examples, which highlight the potential of our approach for designing materials with improved thermomechanical response.     

A large strain thermoviscoplastic formulation for the solidification of S.G. cast iron in a green sand mould

This paper presents a large strain thermoviscoplastic formulation for the analysis of the solidification process of spheroidal graphite (S.G.) cast iron in a green sand mould. This formulation includes two different non-associate constitutive models in order to describe the thermomechanical behaviour of each of such materials during the whole process. The performance of these models is evaluated in the analysis of a solidification test.     

A two-level micromechanical theory for a shape-memory alloy reinforced composite

A two-level micromechanical theory is developed to study the influence of the shape and volume concentration of shape-memory alloy (SMA) inclusions on the overall stress–strain behavior of a SMA-reinforced composite. The first level exists on the smaller SMA level, in which, under the action of stress, parent austenite may transform into martensite. The second level is on the larger scale consisting of the metastable SMA inclusions and an inactive polymer matrix. The evolution of martensite microstructure is evaluated from the irreversible thermodynamics, in conjunction with the micromechanics and physics of martensitic transformation. By taking martensite to exist in the form of thin plates on the micro scale and assuming SMA inclusions to be homogeneously aligned spheroids on the macro scale, the overall stress–strain behaviors of a NiTi-reinforced composite are calculated for various SMA shapes and concentrations. The results indicate that, under a tensile axial loading, martensitic transformation is easier to take place when SMA inclusions exist in the form of long fibers, but most difficult to occur when they are in the form of flat discs. In general the levels of the applied stress at which martensite transformation commences, finishes, and austenitic transformation starts, and finishes, are found to decrease with increasing aspect ratio of the SMA inclusions while the damping capacity increases with it; these properties point to the advantage of using fibrous composites for actuators or sensors under a tensile loading.     

A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

Generalization of the Clausius-Clapeyron equation in a coupled thermomechanical model

Several modifications of the Clausius-Clapeyron equation for deformable media, including solid-phase transformations which depend on the change of additional parameters, are proposed. A model of the medium with tensor concentrations of the components for which the unique Clausius-Clapeyron equation is also valid is proposed. The tensor analog of the transition heat is introduced, and an expression for the total transition heat related to the energies of chemical bonds in the crystal lattice is obtained. At least for slow processes, the fundamental possibility of determining the self transition heat in the experiment is shown analytically. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 103–111, November–December, 1999.     

Cyclic thermomechanical behavior of a polycrystalline pseudoelastic shape memory alloy

In this work, 3D finite element modeling is employed to examine the thermomechanical behavior of a polycrystalline Ni-Ti shape memory alloy in the pseudoelastic regime. It is shown that the tension-compression asymmetry during uniaxial cyclic loading is due to a preferred orientation of the crystallographic texture. In pure shear loading, the thermomechanical behavior exhibits symmetry in both senses of shear, due to the fiber texture of the specimen bar stock. It is also shown that the apparent strain rate-dependence is due to thermomechanical coupling with latent heat generation/absorption during phase transformation.     

A thermomechanical model accounting for the behavior of shape memory alloys in finite deformations

Shape memory alloys (SMA) comport an interesting behavior. They can undertake large strains and then recover their undeformed shape by heating. In this context, one of the aspects that challenged many researchers was the development of a mathematical model to predict the behavior of a known SMA under real-life conditions, or finite strain. This paper is aimed at working out a finite strain mathematical model for a Ni–Ti SMA, under the superelastic experiment conditions and under uniaxial mechanical loading, based on the Zaki–Moumni 3D mathematical model developed under the small perturbations assumption. Within the current article, a comparison between experimental findings and calculated results is also investigated. The proposed finite strain mathematical model shows good agreement with experimental data.     

A constitutive model for shape memory alloys accounting for thermomechanical coupling

This paper presents a generalized Zaki-Moumni (ZM) model for shape memory alloys (SMAs) [cf. Zaki, W., Moumni, Z., 2007a. A three-dimensional model of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55, 2455-2490 accounting for thermomechanical coupling. To this end, the expression of the Helmholtz free energy is modified in order to derive the heat equation in accordance with the principles of thermodynamics. An algorithm is proposed to implement the coupled ZM model into a finite element code, which is then used to solve a thermomechanical boundary value problem involving a superelastic SMA structure. The model is validated against experimental data available in the literature. Strain rate dependence of the mechanical pseudoelastic response is taken into account with good qualitative as well as quantitative accuracy in the case of moderate strain rates and for mechanical results in the case of high strain rates. However, only qualitative agreement is achieved for thermal results at high strain rates. It is shown that this discrepancy is mainly due to localization effects which are note taken into account in our model. Analyzing the influence of the heat sources on the material response shows that the mechanical hysteresis is mainly due to intrinsic dissipation, whereas the thermal response is governed by latent heat. In addition, the variation of the area of the hysteresis loop with respect to the strain rate is discussed. It is found that this variation is not monotonic and reaches a maximum value for a certain value of strain rate.     

A model of the thermomechanical process during welding of plates

A model of the thermomechanical process that takes place as straight plates are welded, with due consideration of the weld seam filling, is developed within the limits of linear thermoelasticity from the temperature dependence of the properties. The filler material is assumed to be unstressed as the weld seam is filled. A modified form of constitutive equations for the filler material is proposed for implementing that assumption within the standard finite-element technique. Some laws of relative plate displacement during welding are investigated and experimental and computed results are compared. Translated from Prikladnaya Mekhanika, Vol. 34, No. 12, pp. 70–76, December, 1998.     

A suspension model for low shear rate polymer solidification

The events during solidification of flowing polymers are extremely complex, often involving partial crystallization. Many processes may need consideration of viscoelastic effects, but here we present an elementary viscous model of solidification rheology based on suspension theory, with application to some recent slow-shearing experiments.It is shown that neither a simple dependence of crystallinity on shear rate nor total shear describes the results, but that a scaling law is evident.